a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

Evaluate the integral to solve for y :



Use the other known value, f(2) = 18, to solve for k :

Then the curve C has equation

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

The slope of the given tangent line
is 1. Solve for a :

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).
Decide which of these points is correct:

So, the point of contact between the tangent line and C is (-1, -3).
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Answer:
Step-by-step explanation:
47 divided by 8
= 5.875
hope this helps
Answer:
(0, -3) and (3, 0)
Explanation:
1st equation: y = x² -2x - 3
2nd equation : y = x - 3
Using substitution method:
x² -2x - 3 = x - 3 <em>exchange sides</em>
x² - 2x - x - 3 + 3 = 0 <em>simplify</em>
x² - 3x = 0 <em> take common factor</em>
x(x - 3) = 0 <em>simplify</em>
x = 0, 3
Solve for y:
when x is 0, y = x - 3 = 0 - 3 = -3
when x is 3, y = x - 3 = 3 - 3 = 0
Answer:
The sum of the series is 3/2
Step-by-step explanation:
Given
1 + 1/3 + 1/3^2 + ....
Required
The sum of the series
This implies that we calculate the sum to infinity.
We have:
-- The first term
First, calculate the common ratio (r)

Change to product

Solve

The sum of the series is then calculated as:


Solve the denominator

Express as product

